Abstract
In an ESA 2011 paper, Couëtoux [2] gives a beautiful \(\frac{3}{2}\)-approximation algorithm for the problem of finding a minimum-cost set of edges such that each connected component has at least k vertices in it. The algorithm improved on previous 2-approximation algorithms for the problem. In this paper, we reanalyze Couëtoux’s algorithm using dual-fitting and show how to generalize the algorithm to a broader class of graph problems previously considered in the literature.
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References
Bazgan, C., Couëtoux, B., Tuza, Z.: Complexity and approximation of the Constrained Forest problem. Theoretical Computer Science 412, 4081–4091 (2011)
Couëtoux, B.: A \(\frac{3}{2}\) Approximation for a Constrained Forest Problem. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 652–663. Springer, Heidelberg (2011)
Goemans, M.X., Williamson, D.P.: Approximating minimum-cost graph problems with spanning tree edges. Operations Research Letters 16, 183–189 (1994)
Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24, 296–317 (1995)
Goemans, M.X., Williamson, D.P.: The primal-dual method for approximation algorithms and its application to network design problems. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-hard Problems, ch. 4. PWS Publishing, Boston (1996)
Imielińska, C., Kalantari, B., Khachiyan, L.: A greedy heuristic for a minimum-weight forest problem. Operations Research Letters 14, 65–71 (1993)
Kruskal, J.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society 7, 48–50 (1956)
Laszlo, M., Mukherjee, S.: Another greedy heuristic for the constrained forest problem. Operations Research Letters 33, 629–633 (2005)
Laszlo, M., Mukherjee, S.: A class of heuristics for the constrained forest problem. Discrete Applied Mathematics 154, 6–14 (2006)
Laszlo, M., Mukherjee, S.: An approximation algorithm for network design problems with downwards-monotone demand functions. Optimization Letters 2, 171–175 (2008)
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Davis, J.M., Williamson, D.P. (2012). A Dual-Fitting \(\frac{3}{2}\)-Approximation Algorithm for Some Minimum-Cost Graph Problems. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_33
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DOI: https://doi.org/10.1007/978-3-642-33090-2_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33089-6
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